A Moscow native, Anikushin began studying piano at age five. At age 11, he entered the Moscow Conservatory, studying under Y.I. Batuyev. After immigrating to the USA in 1991, Anikushin studied with Milton Salkind at the San Francisco Conservatory and received his bachelor's and master's degrees from the Juilliard School as a full scholarship student of Oxana Yablonskaya. Anikushin is currently enrolled in the DMA program at The Manhattan School of Music as the student of Solomon Mikowsky.